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Loewner Matrices

Speaker: Rajendra Bhatia, Professor of Mathematics, Ashoka University

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Abstract:  Given a function f on R, a positive integer n and a choice of points p_1,….,p_n, the Loewner matrix L(f, p) is the nxn matrix whose (i,j) entry is the divided difference [f(p_i) – f(p_j)] / [p_i – p_j]. These matrices arise in several contexts, one of them being the celebrated Loewner’s theory of matrix monotone functions. Some of this theory was discussed in Siddharth Mulherkar’s talk on 6 April. We will talk some more of these matrices. The talk is intended for and will be accessible to, students who have taken a second course on Linear Algebra. The first part will be on the blackboard introducing all concepts involved.

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